Nucleus segmentation is a key component for many digital pathology applications. A great deal of effort has been made to extract the mask of nuclei or cells from an image comprising of these structures, which is essential for the efficient characterization of these structures. A popular nucleus segmentation framework starts with foreground detection of isolated nuclei and nucleus clusters based on global or local thresholding methods [1]. The nucleus clusters are then divided into several nuclei using a type of watershed transform [2,3,4], such as a competitive region growing process for dividing the cluster into plausible subregions, utilizing nucleus seeds generated by the distance transform [8] or a type of radial symmetry transform [5,6], or a type of Hough transform [7], etc. Usually, when the foreground delineation is accurate, the separation of clustered nuclei is plausible. Existing thresholding methods for foreground detection rely on the assumption that the foreground (i.e., the isolated nuclei or nucleus clusters) is consistently brighter (or darker) than the background (i.e., the empty area or unspecific staining area), locally and/or globally. However, in reality, the intensity of the nuclei and nuclei clusters varies a great deal across the same image (or field of view). For instance, unspecific stains in the image may have the same intensity level as isolated nuclei and nucleus clusters. Prior techniques primarily utilize edge detection filters and/or intensity statistics based thresholding; and that was not completely effective because of varying tissue density and staining. See, for example, M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation”, Journal of Electronic Imaging, Vol. 13, No. 1, pp. 146-165, 2004; L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 6, pp. 583-598, 1991; L. Najman and M. Schmitt, “Geodesic saliency of watershed contours and hierarchical segmentation”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 18, No. 12, pages 1163-1173, 1996; J. Cousty, G. Bertrand, L. Najman, and M. Couprie, “Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle”, IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 31, No. 8, pp. 1362-1374, 2009; Hidefumi Kobatake and Shigeru Hashimoto, “Convergence Index Filter for Vector Fields”, IEEE Transactions on Medical Imaging, Vol. 8, No. 8, pp. 1029-1038, August 1999; Bahram Parvin, Qing Yang, Ju Han, Hang Chang, Bjorn Rydberg and Mary Helen Barcellos-Hoff, “Iterative Voting for Inference of Structural Saliency and Characterization of Subcellular Events”, IEEE Transactions on Image Processing, Vol. 16, No. 3, pp. 615-623, March 2007; Duda, R. O. and P. E. Hart, “Use of the Hough Transformation to Detect Lines and Curves in Pictures,” Comm. ACM, Vol. 15, pp. 11-15, 1959; J. Canny, “A computational approach to edge detection”, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 8, No. 6, pp. 679-698, 1986; G. Guy and G. Medioni, “Inferring global perceptual contours from local features,” in International Journal of Computer Vision, 1996, vol. 20, pp. 113-133; L. A. Loss, G. Bebis, M. Nicolescu, A. Skurikhin, “An iterative multi-scale tensor voting scheme for perceptual grouping of natural shapes in cluttered backgrounds,” in Computer Vision and Image Understanding, 2009, vol. 113, pp. 126-149.